When the New York City Education Department lifted a long-held ban on cellphones in school buildings last year, it acquiesced to the omnipresent reality of technology in daily life.

But the change also unleashed tens of thousands of smartphones in the hands of teenagers, eager to gobble away at the nearest Wi-Fi connection like so many hungry termites, eating up their schools’ bandwidth with YouTube streams, Snapchat exchanges and the like. That can leave little capacity for teachers to use the Internet for actual instruction.

Now, at least one school is striking back. At the Bronx High School of Science, the administration has told students not to use the network from their cellphones and has started booting interlopers off, one by one, and blocking their devices from the network.

“We don’t want to exacerbate the problem we already have any more,” Jean Donahue, the principal at Bronx Science, said.

Ms. Donahue noted that the school’s network had been struggling for several years under an increasingly technology-heavy curriculum, and that the Education Department was working with the school to increase its broadband capacity.

“We know,” she added of students’ cellphones, “it doesn’t help.”

Anthony Barbetta, the principal of Townsend Harris, a top high school in Queens, said his school’s network had also seen a cellphone slowdown this year. But so far, he has no plans to address it.

“I definitely think there’s been an impact,” Mr. Barbetta said. “But we haven’t told students they cannot be on the Wi-Fi. I don’t know if that’s enforceable realistically.

“We’re hoping for an upgrade, just like I think everybody else is hoping to get an upgrade.”

Enforcement of the citywide cellphone ban was extremely uneven. At most schools, teachers and administrations looked the other way as long as phones were not flashed directly in front of them. Bags were not searched for contraband phones. But at the many city school buildings with metal detectors, they were not allowed inside.

When Mayor Bill de Blasio’s administration announced last year that schools would be allowed to decide their own cellphone policies going forward, Bronx Science — one of the city’s top high schools, where applicants must pass a test to gain entry — said students could use their phones at lunch and during free periods.

Several Bronx Science students on their way home from school last week said they most frequently used the wireless network to send pictures to their friends on Snapchat, an app they said the school did not block; Facebook, by contrast, was not accessible. This being Bronx Science, some students said they found the wireless most useful for statistics classes, or to use Google Slides to put together school projects.

“A friend once told me he was watching Netflix” at school, said Eugene Park, a senior and Snapchat enthusiast. “Netflix is not blocked, conveniently.”

Miguel Mercado, 16, a junior, said he used the school for YouTube, mostly to listen to music.

A classmate named Phillip, who was standing beside him, gave a snicker.

“What? I like Adele,” Miguel said. “Is there a problem?”

Despite the new rule barring students’ cellphones on the wireless network, Miguel said he was still able to use it on his phone last week. Many of his schoolmates who were unscientifically surveyed said the same.

In 2013, Scott M. Stringer, the Manhattan borough president at the time, criticized the Education Departmentin a report that said 75 percent of school buildings had excruciatingly slow Internet speeds.

Since then, amid a national push to increase the speed and connectivity of schools, the department has upgraded the wiring at more than 250 school buildings, Devora Kaye, a department spokeswoman, said. Ms. Kaye added that the city plans to spend $650 million over the next three years to further upgrade school technology.

At Bronx Science, Ms. Donahue said she was working with the department to improve the school’s broadband capacity. She added that the department had been quite responsive, helping with short-term upgrades while it works toward a more systemic upgrade.

In the meantime, the school was identifying personal mobile devices one by one and blocking them from the network. (Students are still free to use their own data plans, though many complained of spotty service in the building.)

Just changing the password is not an option, said Phoebe Cooper, an assistant principal at the school, “because the kids will figure it out within days.”

“We tried that,” she explained. “A kid found it, wrote it on his hand and put a picture on Facebook.”

And students seemed fairly certain they could stay ahead of administrators, anyway.

“Give it a month and everyone will be back on,” Kevin Zhang, a senior, said. “It’s mostly for a lack of trying that people aren’t on it now.”